18. Find the equation of the circle with center (5, -3) and radius of 3. Show work.

The answers  to all parts are shown below.

One of the most crucial equations in mechanics is the wave equation. It describes the movement of fluid surfaces, such as water waves, in addition to the movement of strings and wires.

Define constants:

t0 = 1.7seconds      h0 = 58cm  highest point

t1 =  4.4 seconds       h1 = 44 cm  lowest point

t2 = 6 seconds    h2 = (h0 + h1)/2 = 51 cm  center height

Half a cycle passes between t0 and t1, so the period T is

T = 2(t1 - t0) = 2(4.4-1.7) seconds = 5.4 seconds

The amplitude A is half the total height change between h0 and h1:

A = (h0 - h1)/2 = 7 cm

a) Equation of motion in terms of height H above the floor is

H(t) = h2 + A Co s[2π(t - t0)/T]    

H(t) = 51 cm + (7cm) Cos[0.1775(t - 1.7second)/second]

b)  Let t = 6 seconds in the equation:

H(t) = 51 cm + (7cm) Cos[0.1775(6 - 1.7second)/second]  

                        = 51 + 7 x (-0.4008)

                        = 48.1944 cm

c)  Let t = 0 seconds in the equation:

H(0 seconds) = 51 cm + (7cm) Cos[0.1775(0 - 1.7second)/second]  

                   = (51+ 7[0.99999986]) cm

                   = 57.99cm      

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Step-by-step explanation:

(6×(-4) - 1 )/ 4=-24-1/4= -25/4= -6.2

The solutions of the system of linear equations 3x+ 4y= 10 2x+ 2y= 2 can be found by using the method of substitution or elimination.Solve one of the equations for one of the variables in terms of the other variable.

Let's solve the first equation for x: 3x + 4y = 10 3x = -4y + 10 x = -4/3y + 10/3

Substitute this expression into the other equation and solve for the remaining variable.

2(-4/3y + 10/3) + 2y = 2 -8/3y + 20/3 + 2y = 2 -8/3y + 2y = -20/3 + 2 -2/3y = -18/3 y = 9

Use the value of y to find the value of x.

x = -4/3y + 10/3 x = -4/3(9) + 10/3 x = -4 + 10/3 x = -4 + 10/3

The solution of the system of equations is (x,y) = (-4 + 10/3, 9)

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Answer:

14.6

Step-by-step explanation:

In the example

x =kh

k is the constant of proportionality

Answer:

would look like the picture down below meaning it has a ZERO slope

Step-by-step explanation:

(a)

[tex] \frac{b + x}{3} = \frac{b - x}{4} \\ 4b + 4x = 3b - 3x \\ b = - 7x[/tex]

(b)

[tex]p = \frac{y}{1 + y \\ } \\ p + py = y \\ y - py = p \\ y = \frac{p}{1 - p} [/tex]

(c)

[tex] \frac{1}{a} = \frac{1}{b} - \frac{1}{c} \\ \frac{1}{c } = \frac{1}{b} - \frac{1}{a} \\ \frac{1}{c} = \frac{a - b}{ab} \\ c = \frac{ab}{a - b} [/tex]

Answer:

using the linear combination method

Step-by-step explanation:

hope this helps

The Golden Rule to Solve an Equation are:-

In arithmetic, an equation is a system that expresses the equality of two expressions, by connecting them with the equals signal =. The phrase equation and its cognates in different languages may additionally have subtly one-of-a-kind meanings; as an example, in French, an équation is defined as containing one or more variables, whilst in English, any well-formed method together with expressions associated with an equals signal is an equation.

solving an equation containing variables includes figuring out which values of the variables make the equality real. The variables for which the equation must be solved are also called unknowns, and the values of the unknowns that fulfill the equality are called answers to the equation. There are kinds of equations: identities and conditional equations. An identity is real for all values of the variables. A conditional equation is handiest authentic for particular values of the variables.

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Total money spent on a pass and lunch for each student = $29.9

A field trip is a journey by a group of people to a place away from their normal environment.

Given :

School spends $633.85 on passes for 31 students and 4 teachers.

School spends $300.08 on lunch for 31 students.

Calculation :

School spends on a pass for each student,

633.85

  35

=20.22$

School spends on a lunch for each student,

300.08

  31

=9.68$

Therefore, total money spent on a pass and lunch for each student

20.22 + 9.68

= $29.9

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There is no relation between hours studying and grades on a test. this statements would be her null hypothesis .

What is the definition of a null hypothesis?

The null hypothesis presupposes that any variation between the selected attributes you observe in a set of data is the result of chance.

                                    For instance, if the predicted profits from the gambling game genuinely equal zero, then any discrepancy between the data's average profits and zero results from chance.

The null hypothesis doesn't exist.

A null hypothesis may declare, for instance, that the population mean return is equal to zero. The null hypothesis is typically an equality hypothesis for population parameters.

                               It might be said that the alternative hypothesis is the exact opposite of a null hypothesis (e.g., the population mean return is not equal to zero).

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The right side of the first equation is 78 and the right side of the second equation is -72. Both sides of the equations are constants (numbers with no variable in them)

The left side of the first equation is 2(3b+6) and the left side of the second equation is -2(6c-3). Both sides of the equations are products of a constant and a variable or a sum/difference of variables.

To find the value of b and c in the equation, you need to solve the equation.

For the first equation:

2(3b + 6) = 78

3b + 6 = 39

3b = 33

b = 11

For the second equation:

-2(6c - 3) = -72

6c - 3 = 36

6c = 39

c = 6.5

So, the value of b is 11 and the value of c is 6.5

The closest to the value of b is 3.6912.

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

f(x)=a(b)^x and we know that f(3)=17 and f(7)=3156. what is the value of b

Set up both equations with values

When x = 3, f(3) = 17, so we have a(b)^3 = 17

When x = 7, f(7) = 3156, so we have a(b)^7 = 3156

Isolate a in each equation

a = 17/(b)^3

a = 3156/(b)^7

Now set them equal to each other

17/(b)^3 = 3156/(b)^7

Cross Multiply

17b^7 = 3156b^3

Divide each side by b^3

17b^4 = 3156

Divide each side by 17

b^4 = 185.6471

b = 3.6912

Therefore, the closest to the value of b is 3.6912.

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The surface area of the right triangular pyramid is 435.5 square units.

What is a surface area of a triangle?

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees. It is the polygon with the fewest sides.

Here, we have

Given: X = 13 units, Y = 11 units, and Z = 15 units

We have to determine the surface area of the right triangular pyramid.

Surface area = base area + 1/2 (perimeter × slant height)

A = xy + 1/2 (3x ×  z)

A = 13 × 11 + 1/2 (3× 13 ×  15)

A = 143 + 292.5

A = 435.5 square units.

Hence, the surface area of the right triangular pyramid is 435.5 square units.

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The values of x and y for the given similar triangles are 3 and 10 respectively.

For the stated question-

Using the similarity for the triangle ABC  and DBE,

Taking the ratios of the sides.

x/9 = 4/12

x = 9/3 = 3

And,

5/y = 4/(12 - 4)

5/y = 4/8

y = 5*2 = 10

Thus, the values of x and y for the given similar triangles are 3 and 10 respectively.

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The four main inverse operations in math are addition, subtraction, multiplication, and division. These are the operations that reverse the effects of the operation.

When you use the word "inverse," you want to move backward in time or space. The Latin term "inversus," which means to turn inside out or upside down, is where the word's name originates. An inverse operation in mathematics is a procedure that reverses the effects of a preceding one.

Multiplication, division, subtraction, and addition are the four fundamental mathematical operations. Subtraction, and vice versa, are the opposites of addition. Division and vice versa are the opposites of multiplication.

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Answer:83

Step-by-step explanation: sum of the angles should be 180

44+53+x=180

x=180-97

x=83

Answer:

Step-by-step explanation:

The addition of three angles in a triangle is 180°.

Therefore, if we add all the angles, it's

180°                   = x + 53° +44 °

180° - ( 53°+44° ) = x

        180°-97°   = x

         83 °        = x

Then the answer is obvious, it's 83°.

After solving, the slope of equation 4x + 2y = -12 is -2.

In the given question, we have to find the slope of 4x + 2y = -12.

The given equation is 4x + 2y = -12.

The general equation of line is y = mx + c, where m is the slope of the line and c is the y-intercept of the line.

To find the slope of the line we have to convert the given equation in the form of general equation.

We have to isolate y.

4x + 2y = -12

Subtract 4x on both side, we get

2y = -4x - 12

Divide by 2 on both side, we get

y = -4/2 x - 12/2

y = -2x - 6

On comparing the equation by general equation, we get

m = -2

Hence, the slope of the equation 4x + 2y = -12 is -2.

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The complete question is:

What is the slope of 4x + 2y = -12?

Answer:

Step-by-step explanation:

step 1:  NUMERATOR:

                                  2 x 22 x (5.25)³

                               = 44 x 144.703125

            Numerator = 6366.9375

step 2: DENOMINATOR:

                                     = 3 x 7

           Denominator    = 21

step 3: CALCULATION:
                                      = numenator / denominator

                                      = 6366.9375 / 21

                        Answer =  303.1875

Answer:

$1.75

Step-by-step explanation:

We take

14 / 8 = $1.75

So, one product cost $1.75

The circumference of cylinder's circular face is 20.09 pi units.

The cylinder's lateral surface area is equal to the circumference of the circular base multiplied by the height. A circle's circumference is 2r and its height is h, so the lateral area is 2rh.

That is LSA =  2 × π × r × h where, r = base radius, and h = height of the cylinder.

Here given,

LSA = 824m²

Height = 40 m

By substituting

824 = 2 x 3.14 x r x 40

824 / 2 x 3.14 x 40 = r

r = 3.2m

Circumference of circular face = 2 π r

By substituting the values,

Circumference = 2 x 3.14 x 3.2

Circumference = 20.09 pi units.

Therefore the circumference of a cylinder with circular face is 20.09 pi units.

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Answer:

x=0

Step-by-step explanation:

-Use (a+b)^2=a^2+2ab+b to expand the expression.
-Cancel equal terms on both sides of the equation
-Swap the sides of the equation
-Divide both sides of the equation by 12
-Solution
x=0

After working 8 hours and grading 9 papers per hour, it is expected Autumn has 11 papers left.

To calculate the number of papers she can grade during this time, let's use the rate provided:

This means in 9 hours she can grade 72 papers.

Now, let's calculate the number of papers left:

Based on this, the total of papers left after working for 8 hours is 11 papers.

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The trigonometric identities for double angles can be used to solve for sin2x, cos2x, and tan2x.

Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles and circles. Trigonometry is used to calculate the measurements of angles, lengths, and areas of different geometric figures. It is also used to solve problems involving forces, motion, and velocity.

Sin2x = (2*15/17)*(-12/17) = -30/289
Cos2x = (2*15/17)*(-5/17) = -30/289
Tan2x = (2*15/17)/(-12/17) = -5/12
Since sinx = 15/17 and x terminates in quadrant 2, then x = -3π/17. The trigonometric identities for double angles can be used to solve for sin2x, cos2x, and tan2x.
Sin2x = 2*sinx*cosx = 2*(15/17)*(-12/17) = -30/289
Cos2x = 2*cosx*cosx - 1 = 2*(-12/17)*(-12/17) - 1 = -5/289
Tan2x = (2*sinx*cosx)/(cosx*cosx - sinx*sinx) = (2*(15/17)*(-12/17))/((-12/17)*(-12/17) - (15/17)*(15/17)) = -5/12

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The four rules of multiplication is explained below.

The term multiplication in math is defined as the process of when you take one number and add it together a number of times

Here we need to define the four rules of multiplication.

Here the first rule of multiplication is written as that any number times zero is always zero.

And the next rule is that any number times one is always the same number.

And the another rule is written as add a zero onto the original number when multiplying by 10.

And if the order of factors does not affect the product then switching the roles of multiplier and multiplicand results in the same answer.

Where the other rule is that products are always positive when multiplying numbers with the same signs.

And the final rule is the products are always negative when multiplying numbers with different signs.

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Answer:

Total no ways can be taken

Step-by-step explanation:

The total change in temperature from 3 PM to 8 PM is 25°C.

The first step is to calculate the temperature difference.

Temperature at 3 PM = 3°C

The temperature at 4 The period2°C

The difference = 3 - (-2) = 3 + 2 =5°C

The second step is to calculate the difference time.

Period from 3 PM to 8 PM:

To find the difference between two numbers, subtract the number with the smallest value from the number with the largest value.

So,

8-3 = 5 hours

The third step is to calculate the total temperature change.

5°C × 5 hours = 25°C.

The total change in temperature from 3 PM to 8 PM is 25°C.

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Step-by-step explanation:

let the mid point be (x, y)

x= (-2-2)/2; y=(1-(-3))/2

please comletd the rest by yourself

Answer: I believe the midpoint of the side AB would be (0.3,0)

Step-by-step explanation:

I hope that helps!

The three angles of the triangle can be found by using the formula for the sum of angles of a triangle, which is 180°. Then, the measure of angle A + angle B + angle C = 180°.

1. Using the sum of angles formula, angle A + angle B + angle C = 180°

2. Use the Law of Cosines to calculate the angle between two sides of the triangle.

3. Subtract the sum of those two angles from 180° to find the measure of the third angle.

The three angles of a triangle can be found using the sum of angles formula, which states that the sum of the angles of a triangle equals 180°. This means that angle A + angle B + angle C = 180°. To find the individual angles, we can use the Law of Cosines which states that c2 = a2 + b2 - 2ab cos C, where C is the angle between two sides of the triangle. This formula allows us to calculate the angle between two sides of the triangle. Once we have calculated the sum of the two angles, we can subtract this sum from 180° to find the measure of the third angle. For example, if the sum of the two angles is 120°, then the third angle would be 180° - 120° = 60°. This method allows us to find the three angles of the triangle with the given vertices.

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It is a downward parabola, which means the height of the ramp decreases as the distance from one side of the ramp increases.

What is the parabola?

A parabola is a symmetric, U-shaped geometric curve that can be defined as the set of all points that are equidistant to a fixed point (the focus) and a fixed line (the directrix). It is a conic section, which means it is the intersection of a plane and a cone. In algebraic terms, a parabola can be defined as the graph of a quadratic equation of the form y = ax^2 + bx + c, where a, b, and c are constants.

The height of a ramp can be modeled by f(x) = -1/2 x − 241 +2, where f(x) is the height of the ramp, in feet, and x is the distance from one side of the ramp. To find the vertex of the parabola, we need to complete the square.

The vertex is located at (-b/2a, f(x) + (b^2-4ac)/4a) = (-1/2, -241 +2) = (0, -240)

This means that the maximum height of the ramp is -240 feet when the distance from one side is 0 feet.

Because the distance cannot be negative, and the ramp is unknown length, the relevant domain is {x | 0 ≤ x ≤ unknown}.

Because the height cannot be negative, and the ramp is unknown tall, the relevant range is {y | 0 ≤ y ≤ unknown }.

The graph is symmetric in the line x = 0. This means that the height from a distance of 0 to an unknown feet away from one side of the ramp is the same as the height from a distance of an unknown to an unknown feet away from one side of the ramp.

It is a downward parabola, which means the height of the ramp decreases as the distance from one side of the ramp increases.

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The number of gallons they buy is directly connected to the size of the propane tank: x + $3.83y = $750.

Using the equal symbol (=) to indicate equivalence, a mathematical equation is a formula that joins two statements. An equation in algebra is a statement of mathematics proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign places the variables 3x + 5 and 14 apart. The relationship between two sentences on either side of a letter is described by a mathematical formula. A single variable, which also serves as the symbol, is frequently present. like in 2x - 4 = 2, for instance.

given

Let the direct variation equation

be x + $3.83y = 750,

Let the direct variation equation be x + $3.83y = 750,

The number of gallons they buy is directly connected to the size of the propane tank: x + $3.83y = $750.

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